 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zpbt01()

 subroutine zpbt01 ( character UPLO, integer N, integer KD, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldafac, * ) AFAC, integer LDAFAC, double precision, dimension( * ) RWORK, double precision RESID )

ZPBT01

Purpose:
``` ZPBT01 reconstructs a Hermitian positive definite band matrix A from
its L*L' or U'*U factorization and computes the residual
norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of
L, and U' is the conjugate transpose of U.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] KD ``` KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The original Hermitian band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See ZPBTRF for further details.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).``` [in] AFAC ``` AFAC is COMPLEX*16 array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by ZPBTRF.``` [in] LDAFAC ``` LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )```

Definition at line 118 of file zpbt01.f.

120 *
121 * -- LAPACK test routine --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 *
125 * .. Scalar Arguments ..
126  CHARACTER UPLO
127  INTEGER KD, LDA, LDAFAC, N
128  DOUBLE PRECISION RESID
129 * ..
130 * .. Array Arguments ..
131  DOUBLE PRECISION RWORK( * )
132  COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * )
133 * ..
134 *
135 * =====================================================================
136 *
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION ZERO, ONE
140  parameter( zero = 0.0d+0, one = 1.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  INTEGER I, J, K, KC, KLEN, ML, MU
144  DOUBLE PRECISION AKK, ANORM, EPS
145 * ..
146 * .. External Functions ..
147  LOGICAL LSAME
148  DOUBLE PRECISION DLAMCH, ZLANHB
149  COMPLEX*16 ZDOTC
150  EXTERNAL lsame, dlamch, zlanhb, zdotc
151 * ..
152 * .. External Subroutines ..
153  EXTERNAL zdscal, zher, ztrmv
154 * ..
155 * .. Intrinsic Functions ..
156  INTRINSIC dble, dimag, max, min
157 * ..
158 * .. Executable Statements ..
159 *
160 * Quick exit if N = 0.
161 *
162  IF( n.LE.0 ) THEN
163  resid = zero
164  RETURN
165  END IF
166 *
167 * Exit with RESID = 1/EPS if ANORM = 0.
168 *
169  eps = dlamch( 'Epsilon' )
170  anorm = zlanhb( '1', uplo, n, kd, a, lda, rwork )
171  IF( anorm.LE.zero ) THEN
172  resid = one / eps
173  RETURN
174  END IF
175 *
176 * Check the imaginary parts of the diagonal elements and return with
177 * an error code if any are nonzero.
178 *
179  IF( lsame( uplo, 'U' ) ) THEN
180  DO 10 j = 1, n
181  IF( dimag( afac( kd+1, j ) ).NE.zero ) THEN
182  resid = one / eps
183  RETURN
184  END IF
185  10 CONTINUE
186  ELSE
187  DO 20 j = 1, n
188  IF( dimag( afac( 1, j ) ).NE.zero ) THEN
189  resid = one / eps
190  RETURN
191  END IF
192  20 CONTINUE
193  END IF
194 *
195 * Compute the product U'*U, overwriting U.
196 *
197  IF( lsame( uplo, 'U' ) ) THEN
198  DO 30 k = n, 1, -1
199  kc = max( 1, kd+2-k )
200  klen = kd + 1 - kc
201 *
202 * Compute the (K,K) element of the result.
203 *
204  akk = zdotc( klen+1, afac( kc, k ), 1, afac( kc, k ), 1 )
205  afac( kd+1, k ) = akk
206 *
207 * Compute the rest of column K.
208 *
209  IF( klen.GT.0 )
210  \$ CALL ztrmv( 'Upper', 'Conjugate', 'Non-unit', klen,
211  \$ afac( kd+1, k-klen ), ldafac-1,
212  \$ afac( kc, k ), 1 )
213 *
214  30 CONTINUE
215 *
216 * UPLO = 'L': Compute the product L*L', overwriting L.
217 *
218  ELSE
219  DO 40 k = n, 1, -1
220  klen = min( kd, n-k )
221 *
222 * Add a multiple of column K of the factor L to each of
223 * columns K+1 through N.
224 *
225  IF( klen.GT.0 )
226  \$ CALL zher( 'Lower', klen, one, afac( 2, k ), 1,
227  \$ afac( 1, k+1 ), ldafac-1 )
228 *
229 * Scale column K by the diagonal element.
230 *
231  akk = afac( 1, k )
232  CALL zdscal( klen+1, akk, afac( 1, k ), 1 )
233 *
234  40 CONTINUE
235  END IF
236 *
237 * Compute the difference L*L' - A or U'*U - A.
238 *
239  IF( lsame( uplo, 'U' ) ) THEN
240  DO 60 j = 1, n
241  mu = max( 1, kd+2-j )
242  DO 50 i = mu, kd + 1
243  afac( i, j ) = afac( i, j ) - a( i, j )
244  50 CONTINUE
245  60 CONTINUE
246  ELSE
247  DO 80 j = 1, n
248  ml = min( kd+1, n-j+1 )
249  DO 70 i = 1, ml
250  afac( i, j ) = afac( i, j ) - a( i, j )
251  70 CONTINUE
252  80 CONTINUE
253  END IF
254 *
255 * Compute norm( L*L' - A ) / ( N * norm(A) * EPS )
256 *
257  resid = zlanhb( '1', uplo, n, kd, afac, ldafac, rwork )
258 *
259  resid = ( ( resid / dble( n ) ) / anorm ) / eps
260 *
261  RETURN
262 *
263 * End of ZPBT01
264 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
complex *16 function zdotc(N, ZX, INCX, ZY, INCY)
ZDOTC
Definition: zdotc.f:83
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
subroutine zher(UPLO, N, ALPHA, X, INCX, A, LDA)
ZHER
Definition: zher.f:135
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhb.f:132
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